H B

b b eBB

FIGURE 6.9 The five frames of a sample (A) habituation, (B) familiar test, and (C) novel test trial in Brannon (2002a). Infants were habituated to one ordinal direction of numerosities and then tested with the same direction and the reversed direction. Achromatic elements are shown here; however, elements were rainbow colored in the actual experiment. (From Brannon, E.M., Cognition, 83, 223, 2002.)

intake, not number of items. Again, more research is needed to explain why different paradigms yield different results. One possibility is that these paradigms involve different representational systems.

6.5.2 Addition and Subtraction

As described above, the violation-of-expectancy paradigm exploits the fact that infants look longer at unexpected outcomes than expected ones. Wynn (1992) first showed that infants form expectations about the number of objects that are successively placed behind an opaque barrier. Infants look longer at the unexpected outcome when tested with 2 - 1 = 1 or 2 (as illustrated in Figure 6.6), 1 + 1 = 1 or 2, and 1 + 1 = 2 or 3. These findings have been replicated and extended in other laboratories (Baillargeon, 1994; Feigenson et al., 2002b; Koechlin et al., 1998; Simon et al., 1995; Wynn, 1995). For example, Simon et al. (1995) replicated the Wynn paradigm but used Elmo dolls in the initial phase of the trials and then surreptitiously replaced Elmo dolls with Ernie dolls. The infants' expectations were not violated by this identity switch; they looked longer only when the result was an unexpected number. This suggests that in some sense infants represent the number of objects stripped of their particular nonnumerical features. In another study, the Wynn paradigm was replicated; however, the dolls were placed on a revolving surface such that the location of the objects changed during a trial (Koechlin et al., 1998). Infants still looked longer at the unexpected outcome. Thus, infants' representations in these tasks do not preserve object identity or location.

In another test of the Wynn paradigm, Feigenson et al. (2002b) tested 7-month-old infants and pitted violations in surface area against violations in number. Infants saw two small objects placed behind a screen. The screen was then lowered to reveal one or two large objects. The outcome of one large object was expected in area and unexpected in number, while the outcome of two large objects was expected in number and unexpected in area. Infants looked longer at the unexpected area outcome than at the unexpected number outcome. These results suggest that information about surface area is preserved and used in the comparison process.

Despite the many replications of the Wynn paradigm described above, Wakely et al. (2000) obtained negative evidence in a 1 + 1 = 1 or 2 and 2 - 1 = 1 or 2 study with 5-month-old infants. The main differences in the methods were the use of an automated display and rigid intertrial intervals. Wynn (2000) suggested that the failure to replicate might result from subtle details in the procedure that did not optimize infants' attention to the displays. More research is needed to resolve this conflict (See also Cohen and Marks, 2002).

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